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Simplifying (7x + 9)(x + 1) = 35 Reorder the terms: (9 + 7x)(x + 1) = 35 Reorder the terms: (9 + 7x)(1 + x) = 35 Multiply (9 + 7x) * (1 + x) (9(1 + x) + 7x * (1 + x)) = 35 ((1 * 9 + x * 9) + 7x * (1 + x)) = 35 ((9 + 9x) + 7x * (1 + x)) = 35 (9 + 9x + (1 * 7x + x * 7x)) = 35 (9 + 9x + (7x + 7x2)) = 35 Combine like terms: 9x + 7x = 16x (9 + 16x + 7x2) = 35 Solving 9 + 16x + 7x2 = 35 Solving for variable 'x'. Reorder the terms: 9 + -35 + 16x + 7x2 = 35 + -35 Combine like terms: 9 + -35 = -26 -26 + 16x + 7x2 = 35 + -35 Combine like terms: 35 + -35 = 0 -26 + 16x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -3.714285714 + 2.285714286x + x2 = 0 Move the constant term to the right: Add '3.714285714' to each side of the equation. -3.714285714 + 2.285714286x + 3.714285714 + x2 = 0 + 3.714285714 Reorder the terms: -3.714285714 + 3.714285714 + 2.285714286x + x2 = 0 + 3.714285714 Combine like terms: -3.714285714 + 3.714285714 = 0.000000000 0.000000000 + 2.285714286x + x2 = 0 + 3.714285714 2.285714286x + x2 = 0 + 3.714285714 Combine like terms: 0 + 3.714285714 = 3.714285714 2.285714286x + x2 = 3.714285714 The x term is 2.285714286x. Take half its coefficient (1.142857143). Square it (1.306122449) and add it to both sides. Add '1.306122449' to each side of the equation. 2.285714286x + 1.306122449 + x2 = 3.714285714 + 1.306122449 Reorder the terms: 1.306122449 + 2.285714286x + x2 = 3.714285714 + 1.306122449 Combine like terms: 3.714285714 + 1.306122449 = 5.020408163 1.306122449 + 2.285714286x + x2 = 5.020408163 Factor a perfect square on the left side: (x + 1.142857143)(x + 1.142857143) = 5.020408163 Calculate the square root of the right side: 2.240626734 Break this problem into two subproblems by setting (x + 1.142857143) equal to 2.240626734 and -2.240626734.Subproblem 1
x + 1.142857143 = 2.240626734 Simplifying x + 1.142857143 = 2.240626734 Reorder the terms: 1.142857143 + x = 2.240626734 Solving 1.142857143 + x = 2.240626734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = 2.240626734 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = 2.240626734 + -1.142857143 x = 2.240626734 + -1.142857143 Combine like terms: 2.240626734 + -1.142857143 = 1.097769591 x = 1.097769591 Simplifying x = 1.097769591Subproblem 2
x + 1.142857143 = -2.240626734 Simplifying x + 1.142857143 = -2.240626734 Reorder the terms: 1.142857143 + x = -2.240626734 Solving 1.142857143 + x = -2.240626734 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + x = -2.240626734 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + x = -2.240626734 + -1.142857143 x = -2.240626734 + -1.142857143 Combine like terms: -2.240626734 + -1.142857143 = -3.383483877 x = -3.383483877 Simplifying x = -3.383483877Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.097769591, -3.383483877}
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